On the decomposition method to the heat equation with non‐linear and non‐local boundary conditions-Reference-Cited by-同舟云学术

On the decomposition method to the heat equation with non‐linear and non‐local boundary conditions

Published:1998-06-01 Issue:4 Volume:27 Page:426-434
ISSN:0368-492X
Container-title:Kybernetes
language:en
Short-container-title:

Author:

Hadizadeh M.,Maleknejad K.

Abstract

The Adomian decomposition method is used and applied to the mathematical model of a biosensor. This model consists of a heat equation with non‐linear and non‐local boundary conditions. To obtain a canonical form of Adomian, an equivalent non‐linear Volterra integral equation with a weakly singular kernel is set up. In addition, the asymptotic behaviour of the solution as t → 0 and t → • by asymptotic decomposition is obtained. Finally, numerical results are given which support the theoretical results.

Publisher

Emerald

Subject

Computer Science (miscellaneous),Social Sciences (miscellaneous),Theoretical Computer Science,Control and Systems Engineering,Engineering (miscellaneous)

Reference23 articles.

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2. Abbaoui, K. and Cherruault, Y. (1994b), “Convergence of Adomian’s method applied to nonlinear equations”, Mathl. Comput. Modelling, Vol. 20 No. 9, pp. 69‐73.

3. Abbaoui, K. and Cherruault, Y. (1995), “New ideas for proving convergence of decomposition methods”, Computers Math. Applic., Vol. 29 No. 7, pp. 103‐8.

4. Adomian, G. (1990), “A review of the decomposition method and some recent results for nonlinear equations”, Mathl. Comput. Modelling, Vol. 13 No. 7, pp. 17‐34.

5. Adomian, G. (1994a), “Solution of physical problems by decomposition”, Computers Math. Applic., Vol. 27 No. 9/10, pp. 145‐54.

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